ROM stands for Read Only Memory. It is the image of the actual game; for example: Super Smash Bros. This is basically a file that has been converted from a game cartridge or CD so that you can run it on your computer.

Certain emulators run certain ROMs better, depending on their compatibility, so try running the ROM with different emulators. If the ROM still doesn't work, it's most likely that it's corrupt (not playable).